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- W2625688488 abstract "Abstract We consider the problem of analyzing the topology of scalar fields defined on a triangulated shape by using a multi-scale approach, which allows reducing storage costs and computation times, and supports interactive inspection and classification of topological features. We define and implement a multi-scale model that we call a Hierarchical Forman Triangulation (HFT) , where a 3D shape or a terrain is discretized as a triangle mesh, and its topology is described by defining a discrete Morse gradient field based on function values given at the vertices of the mesh. We introduce a new edge contraction operator, which does not change the behavior of the gradient flow and does not create new critical points, and we apply it in combination with a topological simplification operator which eliminates critical elements in pair. By combining the two operators in a sequence, we generate the HFT . We discuss and implement a compact encoding for the HFT that has a lower storage cost with respect to the triangle mesh at full resolution. We show the effectiveness of this new hierarchical model by extracting representations of terrains and shapes endowed with a scalar field at different, uniform and variable, scales and by efficiently computing topological features and segmentations." @default.
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- W2625688488 date "2017-08-01" @default.
- W2625688488 modified "2023-10-18" @default.
- W2625688488 title "Hierarchical Forman Triangulation: A multiscale model for scalar field analysis" @default.
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- W2625688488 doi "https://doi.org/10.1016/j.cag.2017.05.015" @default.
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